multiply the exponents
for example, (2^3)^5 = 2^(3*5) = 2^15
why?
2^3 = 2*2*2
(2^3)^5 = 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2
^ is just shorthand for ***...
Just as * is shorthand for +++...
2*3*4 = 2+2+2 + 2+2+2 + 2+2+2 + 2+2+2
4 to the 10th over 5 to the 5th
4 to the 4th over 5
4 to the 21st over 5 to the 6th
12 to the 7th over 15 squared
for example, (2^3)^5 = 2^(3*5) = 2^15
why?
2^3 = 2*2*2
(2^3)^5 = 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2
^ is just shorthand for ***...
Just as * is shorthand for +++...
2*3*4 = 2+2+2 + 2+2+2 + 2+2+2 + 2+2+2
Let's start with the numerator:
4^7 means 4 raised to the power of 7.
To calculate this, we multiply 4 by itself 7 times: 4 * 4 * 4 * 4 * 4 * 4 * 4.
The result is 16384.
Next, let's simplify the denominator:
5^2 means 5 raised to the power of 2.
To calculate this, we multiply 5 by itself 2 times: 5 * 5.
The result is 25.
Now, we have (16384 / 25)^3.
To simplify this further, we'll raise the fraction to the power of 3.
To raise a fraction to a power, we raise both the numerator and denominator to that power:
(16384^3) / (25^3)
To calculate 16384^3, we multiply 16384 by itself 3 times: 16384 * 16384 * 16384.
The result is 4,398,046,511,104.
To calculate 25^3, we multiply 25 by itself 3 times: 25 * 25 * 25.
The result is 15,625.
Therefore, the expression simplifies to:
4,398,046,511,104 / 15,625
The expression can be written as:
((4^7) / (5^2))^3
Step 1: Simplify the numerator: 4^7 = 16384
Step 2: Simplify the denominator: 5^2 = 25
The expression becomes:
(16384 / 25)^3
Step 3: Simplify the enclosed expression: 16384 / 25 = 655.36
The expression becomes:
(655.36)^3
Step 4: Evaluate the expression: (655.36)^3 = 288,717,436.16
Therefore, the simplified expression is:
288,717,436.16